I was wondering if dark matter could be matter in a 4 (or more)-dimensional space, so instead of coordinates x,y,z it is w,x,y,z. Ordinary matter is at w=0, while dark matter has some distance to ordinary matter in this 4th dimension. Adding a 4th dimension to gravity formulas is straightforward. We would feel the gravity of such matter on distances comparable to the w value of this matter.

If the dark matter's w value would become similar to ours it would suddenly appear in our 3-dimensional space. Since we never observed it the w value might be fixed. For example this could be galaxies in parallel universes. They would feel each others gravity and drag each other along with ech other, but otherwise they are invisible to each other.